The IM construction presented here is unique in the sense that it is not based on an association determined by a statistical model. Instead, the generalized association is made through some very basic distributional properties resulting from the apparently innocuous assumption of exchangeability. This begs the question if this “model-free” form of generalized association can be used in the context of statistical inference as opposed to prediction. A first step would be the development of IM-based solutions to the classical nonparametric problems, e.g., inference on quantiles without distributional assumptions, moving on to more modern/complex problems. Closely related to inference is that of assessing the quality or appropriateness of a posited statistical model, and here conformal-type methods have already proved to be useful [1]}, [2]}.
That is, since a model is judged to be “good” only if it predicts the observed data reasonably well, methods that provide high-quality prediction can be leveraged to provide equally high-quality model assessment. The work in the present paper provides a starting point for the construction of IM-based procedures for valid model assessment. More generally, while IMs had previously focused on classical problems with a fully specified statistical model,
the work presented in this paper reveals an opportunity for IMs to play a role in solving modern problems where valid inference/prediction is required with as few model assumptions as possible.
